#### Volume 22, issue 5 (2018)

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Exotic open $4$–manifolds which are nonleaves

### Carlos Meniño Cotón and Paul A Schweitzer

Geometry & Topology 22 (2018) 2791–2816
##### Abstract

We study the possibility of realizing exotic smooth structures on finitely punctured simply connected closed $4$–manifolds as leaves of a codimension-one foliation on a compact manifold. In particular, we show the existence of uncountably many smooth open $4$–manifolds which are not diffeomorphic to any leaf of a codimension-one ${C}^{2}$ foliation on a compact manifold. These examples include some exotic ${ℝ}^{4}$’s and exotic cylinders ${S}^{3}×ℝ$.

##### Keywords
exotic $\mathbb{R}^4$, nonleaves, codimension-one foliations
##### Mathematical Subject Classification 2010
Primary: 37C85, 53C12, 57R30
Secondary: 57R55
##### Publication
Received: 25 November 2016
Revised: 13 November 2017
Accepted: 25 February 2018
Published: 1 June 2018
Proposed: Yasha Eliashberg
Seconded: András I Stipsicz, Leonid Polterovich
##### Authors
 Carlos Meniño Cotón Departamento de Análise, Instituto de Matemática e Estatística Universidade Federal Fluminense Niterói Rio de Janeiro-RJ Brazil Paul A Schweitzer Departamento de Matemática Pontificia Universidade Católica do Rio de Janeiro Gávea Rio de Janeiro-RJ Brazil